Configurations defined by six lines in space of three dimensions

1933 ◽  
Vol 29 (1) ◽  
pp. 52-68 ◽  
Author(s):  
J. A. Todd
Keyword(s):  
Linear System ◽  
Classical Problem ◽  
Three Dimensions ◽  
Quartic Surface ◽  
Lines In Space ◽  
Pass Through ◽  
Quartic Surfaces

The investigations which follow were originally suggested by the now classical problem of Cayley, the determination of the condition that seven lines in space, of which no two intersect, should lie on a quartic surface. This problem suggests the consideration of the linear system of quartic surfaces which pass through six given lines, and this, essentially, is the basis of all that follows.

scholarly journals On a set of quartic surfaces in space of four dimensions; and a certain involutory transformation

1926 ◽  
Vol 110 (756) ◽  
pp. 700-708
Keyword(s):  
Present Note ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quartic Surface ◽  
Four Dimensions ◽  
Cubic Surfaces ◽  
Mutual Relations ◽  
Quartic Surfaces ◽  
Three Dimensional Space

There exists in space of four dimensions an interesting figure of 15 lines and 15 points, first considered by Stéphanos (‘Compt. Rendus,’ vol. 93, 1881), though suggested very clearly by Cremona’s discussion of cubic surfaces in three-dimensional space. In connection with the figure of 15 lines there arises a quartic surface, the intersection of two quadrics, which is of importance as giving rise by projection to the Cyclides, as Segre has shown in detail (‘Math. Ann.,’ vol. 24, 1884). The symmetry of the figure suggests, howrever, the consideration of 15 such quartic surfaces; and it is natural to inquire as to the mutual relations of these surfaces, in particular as to their intersections. In general, two surfaces in space of four dimensions meet in a finite number of points. It appears that in this case any two of these 15 surfaces have a curve in common; it is the purpose of the present note to determine the complete intersection of any two of these 15 surfaces. Similar results may be obtained for a system of cubic surfaces in three dimensions, corresponding to those here given for this system of quartic surfaces in four dimensions, since the surfaces have one point in common, which may be taken as the centre of a projection.

Complexes of Conics and the Weddle Surface

1924 ◽  
Vol 22 (3) ◽  
pp. 201-216
Author(s):  
C. G. F. James
Keyword(s):  
Arbitrary Point ◽  
Three Dimensions ◽  
Irreducible Curve ◽  
Quartic Surface ◽  
Ordinary Space ◽  
Four Dimensions ◽  
Interesting Connection ◽  
Linear Complexes ◽  
Pass Through ◽  
Do So

A complex or system ∞3 of conics in space of four dimensions is such that a finite number of conics pass through an arbitrary point. Linear complexes are those for which this number is unity, and are such that their curves are defined by conditions of incidence with fixed surfaces, curves and points. In this paper are discussed briefly the linear complexes defined by the condition that their curves meet an irreducible curve in four points. Denoting by a curve of order m and genus p it is found that the curves in question are The complex associated with is considered in greater detail, since it is found to have an interesting connection with the well-known Weddle quartic surface of ordinary space. In fact the conics of the system touching a space (of three dimensions) do so in the points of such a surface. The main properties of this surface can be thence deduced. In addition we discuss certain results in connection with this curve . The paper closes with certain enumerative results which were obtained in the course of the researches giving the results recorded and which we believe are worth record.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

On Five Lines, in Space of Four Dimensions, which lie upon a, Quadric Threefold and the Normal Quartic Curves of which they are Chords

1924 ◽  
Vol 22 (2) ◽  
pp. 189-199
Author(s):  
F. Bath
Keyword(s):  
Three Dimensions ◽  
Apparent Contradiction ◽  
Four Dimensions ◽  
Quartic Curve ◽  
Lines In Space ◽  
Quadric Threefold ◽  
Quartic Curves

The connexion between the conditions for five lines of S4(i) to lie upon a quadric threefold,and (ii) to be chords of a normal quartic curve,leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.

scholarly journals SUBSTANTIATION OF THE FORM AND DETERMINATION OF THE CONSTRUCTIVE PARAMETERS OF THE ROTATION ROLLER OF SOIL

2018 ◽  
Vol 13 (3) ◽  
pp. 72-76
Author(s):  
Гумар Булгариев ◽  
Gumar Bulgariev ◽  
Геннадий Пикмуллин ◽  
Gennadiy Pikmullin ◽  
Ильгиз Галиев ◽  
...  
Keyword(s):  
Analytical Study ◽  
Point Of View ◽  
Design Parameters ◽  
Industrial Complex ◽  
Stage Of Development ◽  
Pass Through ◽  
Spiral Plate ◽  
Working Device ◽  
Important Design

At the present stage of development of the country’s agro-industrial complex, the technological process of surface tillage by combined soil-cultivating machines, simultaneously combining a number of operations in one pass through the field, causes the presence in their designs of the necessary set of various promising working organs. In view of the foregoing, a rotary soil ripper with a spiral-plate working member equipped with radially directed teeth and connected by means of rods with end flanges has been developed. Also, the researched ripper has the limits of penetration of the working element in the form of flat discs equipped with flanges and the radial stop have the ability to rotate around their axes independently of the ripper shaft. An analytical study of the working units of this ripper was carried out from the point of view of the influence of their size and teeth on the process of interaction with the soil, on the basis of which some of their parameters were determined. In conclusion, it was concluded that the analytical equations obtained allow us to justify the choice of the most important design parameters of the proposed new design and design a toothed rotary working device that reduces to constructive implementation after calculating their basic dimensions.

Determination of the Permeability Tensor of Fibrous Reinforcements for VARTM

1999 ◽  
Author(s):  
Pavel B. Nedanov ◽  
Suresh G. Advani ◽  
Shawn W. Walsh ◽  
William O. Ballata
Keyword(s):  
Constant Pressure ◽  
Permeability Tensor ◽  
Three Dimensions ◽  
Resin Flow ◽  
Flow Front ◽  
Resin Impregnation ◽  
Permeable Media ◽  
Front Position ◽  
Transverse Permeability

Abstract VARTM and SCRIMP composite manufacturing processes use a highly permeable media to distribute the resin through the thickness of the composite. Hence, manufacturing simulations of resin flow in such processes requires reliable data for in-plane as well as transverse permeability. The goal of this study is to propose a method for simultaneous determination of the principal values of 3D-permeability tensor of fibrous reinforcements. The permeability components are calculated from experimental data, consisting of flow front position with time during resin impregnation in three dimensions from a radial source under constant pressure using the SMARTweave [Walsh (1993), Fink et al.(1995)] sensor system. Experimental results are compared with numerical simulation.

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

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